**Scalar Multiplication**

Calculate c <a, b>

**15.21** Express *c*<*a,b*> in component form, assuming *a*, *b*, and *c* are real numbers.

The vector <*a,b*> is multiplied by a real number *c*; that real number is called a scalar. To multiply a vector in component form by a scalar value, multiply each of the components by the scalar. In this example, multiply both *a* and *b* by *c*.

A vector has a value (magnitude) and a direction. A scalar only has a value. However, that value changes the SCALE of the vector. For example, multiplying a vector by the scalar 2 doubles its length.

*c*<*a,b*> = <*ca*, *cb*>

**15.22** Express the vector in component form: 3<4,7>.

Multiply each of the components of vector <4,7> by 3.

**15.23** Express the vector in component form: –5<–1,8>.

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